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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics.

Kadierdan Kaheman1, J Nathan Kutz2, Steven L Brunton1

  • 1Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|November 20, 2020
PubMed
Summary
This summary is machine-generated.

We introduce SINDy-PI, a robust algorithm for identifying nonlinear dynamics from noisy data. This method significantly enhances the discovery of implicit ordinary and partial differential equations previously unattainable.

Keywords:
model selectionoptimizationrational differential equationssystem identification

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Area of Science:

  • Dynamical Systems Theory
  • Computational Physics
  • Applied Mathematics

Background:

  • Accurate modeling of nonlinear dynamics from measurement data is crucial but challenging.
  • Existing sparse identification of nonlinear dynamics (SINDy) algorithms struggle with noisy data and implicit/rational functions.
  • Previous extensions to SINDy are highly sensitive to noise, limiting their applicability.

Purpose of the Study:

  • To develop a robust variant of the SINDy algorithm for identifying implicit dynamics and rational nonlinearities.
  • To create a framework that is significantly more noise-robust than existing methods.
  • To enable the identification of complex dynamical systems previously inaccessible to SINDy.

Main Methods:

  • Development of the SINDy-PI (parallel, implicit) algorithm.
  • Integration of multiple optimization algorithms within the SINDy-PI framework.
  • Implementation of a principled approach for model selection.

Main Results:

  • SINDy-PI demonstrates superior noise robustness, orders of magnitude better than previous approaches.
  • Successfully identified implicit ordinary and partial differential equations and conservation laws from noisy, limited data.
  • Enabled the identification of dynamics for systems like the double pendulum and a simplified Belousov-Zhabotinsky reaction model.

Conclusions:

  • SINDy-PI offers a robust and versatile solution for discovering complex nonlinear dynamical systems from data.
  • The algorithm overcomes limitations of previous SINDy variants, particularly in noisy conditions and for implicit/rational dynamics.
  • This advancement opens new possibilities for modeling previously intractable scientific phenomena.